This paper provides an overview of the key values that we argue should underpin an index of the legitimacy of the governance of online intermediaries. The aim is ultimately to allow scholars to rank the policies and practices of intermediaries against core human rights values and principles of legitimate governance in a way that enables comparison across different intermediaries and over time. This work builds on the efforts of a broad range of researchers already working to systematically investigate the governance of social media platforms and telecommunications intermediaries. In this paper, we present our review and analysis of the work that has been carried out to date, using the digital constitutionalism literature to identify opportunities for further research and collaboration.The theme of this special issue is the deeply contested political question of how human rights should be protected in a digital environment. 'Digital constitutionalism' encompasses "a constellation of initiatives that have sought to articulate a set of political rights, governance norms, and limitations on the exercise of power on the Internet" (Gill et al., 2015: 2). One of the key challenges of the digital constitutionalism project is to articulate appropriate limits on the private exercise of power by online intermediaries, how those limits may be imposed, and by whom. This is a complex problem, and requires a new understanding of constitutionalism in an era where regulation is not only, or even not primarily, done by the state (Black, 2001). We take a broad view of 'governance' that encompasses all 'organized efforts to manage the course of events in a social system ' (Burris et al., 2008: 3). This broad definition focuses attention particularly on the policies and practices of online intermediaries as key actors in the governance of online behaviour.Intermediaries play a critical role in governing the internet by developing and managing its infrastructure. By 'intermediaries', we mean the broad range of entities that "bring together or facilitate transactions between third parties on the Internet" (OECD, 2010: 9). Intermediaries of all types ---the owners of physical pipes, the providers of core routing services, the search engines that make content visible, the content hosts, and the social media platforms ---all shape how people communicate in important but different ways. They are the focal points of control, where pressure can be most effectively deployed to influence user behavior (Goldsmith and Wu, 2006), and the decisions that they make have a real impact on public culture and the social and political lives of their users (DeNardis, 2014). In order to progress the political project of digital constitutionalism, more needs to be known about how intermediaries govern their networks and how their decisions impact the basic rights of individuals in different contexts. In this paper, we present an outline of the values we suggest ought to be measured, a guide to the work that has already been completed, and a sketch for futu...